The production function of a firm will change whenever :

The production function represents the technical relationship between physical inputs and the maximum obtainable output [2]. It is defined for a given state of technology [2]. When technology improves, the maximum level of output obtainable for different input combinations increases, resulting in a new production function [1]. Changes in input prices (Option 1) do not alter the production function itself, as the function relates physical quantities and abstracts from prices and costs [6]. Similarly, employing more inputs (Option 2) or increasing the level of output (Option 3) represents a movement along the existing production function or a change in the scale of production within the same technical framework [5]. Only a change in the relevant technology shifts the underlying relationship, thereby changing the production function [6].

Sources

1. [1] Microeconomics (NCERT class XII 2025 ed.) > Chapter 3: Production and Costs > Chapter 3 > p. 37
2. [2] Microeconomics (NCERT class XII 2025 ed.) > Chapter 3: Production and Costs > Chapter 3 > p. 36
3. [6] https://en.wikipedia.org/wiki/Production_function
4. [3] Microeconomics (NCERT class XII 2025 ed.) > Chapter 3: Production and Costs > Cobb-Douglas Production Function > p. 43
5. [4] Microeconomics (NCERT class XII 2025 ed.) > Chapter 3: Production and Costs > 3.6 RETURNS TO SCALE > p. 42
6. [5] Microeconomics (NCERT class XII 2025 ed.) > Chapter 3: Production and Costs > 3.5 SHAPES OF TOTAL PRODUCT, MARGINAL PRODUCT AND AVERAGE PRODUCT CURVES > p. 41